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Choose Resistors to Minimize Errors in Grounded-Load Current Source
By David Guo
Operational amplifiers are frequently used to make high-quality current sources in a variety of applications, such as industrial process control, scientific instrumentation, and medical equipment. Single Amplifier Current Sources , published in Analog Dialogue, Volume 1, Number 1, 1967, introduces several current source circuits that provide a constant current through floating loads or grounded loads. In industrial applications, such as pressure transmitters and gas detectors, these circuits are widely used to provide 4-mA to 20-mA or 0-mA to 20-mA currents.
The improved Howland current source, shown in Figure 1, is very popular because it can drive a grounded load. The transistor, which allows relatively high currents, can be replaced by a MOSFET to achieve even higher currents. For low cost, low current applications, the transistor can be eliminated, as shown in Difference Amplifier Forms Heart of Precision Current Source , published in Analog Dialogue, Volume 43, Number 3, 2009.
The accuracy of this current source is determined by the amplifier and the resistors. This article shows how to choose the external resistors to minimize errors.
Figure 1. Improved Howland current source drives grounded loads.
Analysis of the improved Howland current source yields the transfer function:
Tip 1: Set R2 + R5 = R4
In Equation 1, the load resistance influences the output current, but if we set R1 = R3 and R2 + R5 = R4, the formula reduces to:
Here, the output current is only a function of R3, R4, and R5. With an ideal amplifier, the resistor tolerances determine the accuracy of output current.
Tip 2: Set RL = n × R5
If R5 = RL, it further simplifies to:
Here, the output current depends only on the resistance of R5.
In some cases, the input signal may need to be attenuated. For example, with a 10-V input signal and R5 = 100 Ω, the output current would be 100 mA. To get a 20-mA output current, set R1 = R3 = 5R2 = 5R4. Now, Equation 1 reduces to:
If RL = 5R5 = 500 Ω, then:
Tip 3: Larger value for R1/R2/R3/R4 improves the current accuracy
In most cases, R1 = R2 = R3 = R4, but RL ≠ R5, so the output current is as shown in Equation 3. With R5 = 100 Ω and
Figure 2. Relationship between R1 and output current accuracy.
Tip 4: Resistor tolerance affects current accuracy
Figure 3. Example circuit for IOUT = 1 mA.
Table 1. Worst Case Output Current Error (%) vs. Resistor Tolerance (%)
Loe, James M. Grounded-load current source uses one operational amplifier, Analog Dialogue, Volume 1, Number 3, 1967.
Miller, Bill. Single Amplifier Current Sources , Analog Dialogue, Volume 1, Number 1, 1967.
Moghimi, Reza. Ways to Optimize the Performance of a Difference Amplifier , AN-589.
Zhao, Neil, Reem Malik, and Wenshuai Liao. Difference Amplifier Forms Heart of Precision Current Source , Analog Dialogue, Volume 43, Number 3, 2009.
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